The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two: M.Boij, G.Fløystad -- Koszul Cycles: W.Bruns, A.Conca, T.Römer -- Boij-Söderberg Theory: D.Eisenbud, F.-O.Schreyer -- Powers of Componentwise Linear Ideals: J.Herzog, T.Hibi, H.Ohsugi -- Modules With 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A.: J.Kamnitzer, C.Sadanand -- Realization Spaces for Tropical Fans: E.Katz, S.Payne -- A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus: D.Laksov -- Theory and Applications of Lattice Point Methods for Binomial Ideals: E.Miller -- Equations Defining Secant Varieties: Geometry and Computation: J.Sidman, P. Vermeire.

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field.  This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions.   The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.